Math Problem Statement

Find three consecutive integers with a sum of 93.

Solution

The problem asks for three consecutive integers whose sum is 93. Let's solve it step by step.

Let the three consecutive integers be:

  • xx (the first integer),
  • x+1x+1 (the second integer),
  • x+2x+2 (the third integer).

Their sum is: x+(x+1)+(x+2)=93x + (x+1) + (x+2) = 93

Simplify: 3x+3=933x + 3 = 93

Subtract 3 from both sides: 3x=903x = 90

Divide by 3: x=30x = 30

The integers are: 30,31,3230, 31, 32

Would you like more details, or do you have any further questions?

Related Questions:

  1. How would the solution change if the sum was 105 instead of 93?
  2. Can you derive a general formula for finding consecutive integers with a given sum?
  3. What happens if we deal with consecutive even integers instead?
  4. Could this problem be solved graphically? How?
  5. How can you extend this to four consecutive integers?

Tip: Always check your final answer by adding the integers to verify the sum!

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Math Problem Analysis

Mathematical Concepts

Algebra
Consecutive Integers
Equations

Formulas

Sum of consecutive integers: x + (x+1) + (x+2) = S

Theorems

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Suitable Grade Level

Grades 6-8